Leetcode 有效的数独

地址：https://leetcode-cn.com/explore/interview/card/top-interview-questions-easy/1/array/30/

题目

判断一个 9x9 的数独是否有效。只需要根据以下规则，验证已经填入的数字是否有效即可。

1. 数字 1-9 在每一行只能出现一次。
2. 数字 1-9 在每一列只能出现一次。
3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。

上图是一个部分填充的有效的数独。

数独部分空格内已填入了数字，空白格用 '.' 表示。

示例 1:

输入:
[
  ["5","3",".",".","7",".",".",".","."],
  ["6",".",".","1","9","5",".",".","."],
  [".","9","8",".",".",".",".","6","."],
  ["8",".",".",".","6",".",".",".","3"],
  ["4",".",".","8",".","3",".",".","1"],
  ["7",".",".",".","2",".",".",".","6"],
  [".","6",".",".",".",".","2","8","."],
  [".",".",".","4","1","9",".",".","5"],
  [".",".",".",".","8",".",".","7","9"]
]
输出: true

示例 2:

输入:
[
  ["8","3",".",".","7",".",".",".","."],
  ["6",".",".","1","9","5",".",".","."],
  [".","9","8",".",".",".",".","6","."],
  ["8",".",".",".","6",".",".",".","3"],
  ["4",".",".","8",".","3",".",".","1"],
  ["7",".",".",".","2",".",".",".","6"],
  [".","6",".",".",".",".","2","8","."],
  [".",".",".","4","1","9",".",".","5"],
  [".",".",".",".","8",".",".","7","9"]
]
输出: false
解释: 除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。
     但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。

说明:

• 一个有效的数独（部分已被填充）不一定是可解的。
• 只需要根据以上规则，验证已经填入的数字是否有效即可。
• 给定数独序列只包含数字 1-9 和字符 '.' 。
• 给定数独永远是 9x9 形式的。

我的解决方案

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        bool isValid = true;
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {    //判断i行
                if (board[i][j] == '.')
                    continue;
                for (int k = j + 1; k < 9; k++) {
                    if (board[i][k] == '.')
                        continue;
                    if (board[i][j] == board[i][k]) {  //如果i行有两个数字相等跳转至函数返回语句
                        isValid = false;   //置isValid为false
                        goto label;   //并跳转至函数返回语句
                    }
                }
            }
            for (int j = 0; j < 9; j++) {    //判断i列
                if (board[j][i] == '.')
                    continue;
                for (int k = j + 1; k < 9; k++) {
                    if (board[k][i] == '.')
                        continue;
                    if (board[j][i] == board[k][i]) {
                        isValid = false;
                        goto label;
                    }
                }
            }
        }
        for (int i = 0; i < 9; i += 3) {    //判断3x3宫内
            for (int j = 0; j < 9; j += 3) {   //前两层循环用于遍历每个3x3宫格的左上角元素所在位置
                vector<int> vec(10);  //事实上只用到vec[1]~vec[9]，用于记录3x3宫格内每个数字出现的次数
                for (int k = i; k < i + 3; k++) {   //后两层循环用于遍历以board[i][j]作为左上角元素的3x3宫格
                    for (int l = j; l < j + 3; l++) {
                        int num = board[k][l] - 48;   //将字符转换为数字
                        if (num >= 1 && num <= 9){   //判断字符是否是数字
                            vec[num]++;    //如果是数字，就以这个数字作为下标将vec[num]加一，表示num出现的次数
                            if (vec[num] > 1) {  //vec[num]>1说明这个数字重复出现了
                                isValid = false;   //置isValid为false
                                goto label;   //并跳转至函数返回语句
                            }
                        }
                    }
                }
            }
        }
    label:
    return isValid;
    }
};